{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 可视化三维样本数据点的PCA过程"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from mpl_toolkits import mplot3d\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# 在三维空间随机生成100个样本点\n",
    "np.random.seed(6666)\n",
    "X = np.random.random(size=(100, 3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10695b208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = plt.axes(projection='3d')\n",
    "ax.scatter3D(X[:,0], X[:,1], X[:,2])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def f(w, X):\n",
    "    return np.sum((X.dot(w)**2)) / len(X)\n",
    "\n",
    "def df(w, X):\n",
    "    return X.T.dot(X.dot(w)) * 2. / len(X)\n",
    "\n",
    "def direction(w):\n",
    "    return w / np.linalg.norm(w)\n",
    "\n",
    "def first_component(X, initial_w, eta, n_iters = 1e4, epsilon=1e-8):\n",
    "    \n",
    "    w = direction(initial_w) \n",
    "    cur_iter = 0\n",
    "\n",
    "    while cur_iter < n_iters:\n",
    "        gradient = df(w, X)\n",
    "        last_w = w\n",
    "        w = w + eta * gradient\n",
    "        w = direction(w) \n",
    "        if(abs(f(w, X) - f(last_w, X)) < epsilon):\n",
    "            break\n",
    "            \n",
    "        cur_iter += 1\n",
    "\n",
    "    return w"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.61952027, 0.55653544, 0.55359095])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "initial_w = np.random.random(X.shape[1])\n",
    "eta = 0.01\n",
    "w1 = first_component(X, initial_w, eta) \n",
    "w1 # 求出第一主成分"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 将原来的所有样本点X去除在第一主成分上的分量，得到X2\n",
    "X2 = np.empty(X.shape)\n",
    "for i in range(len(X)):\n",
    "    X2[i] = X[i] - X[i].dot(w1) * w1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10696ff28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 绘制X2，此时，X2的所有样本点分布在一个平面上\n",
    "ax = plt.axes(projection='3d')\n",
    "ax.scatter3D(X2[:,0], X2[:,1], X2[:,2])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.71119474,  0.69644447,  0.0957452 ])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w2 = first_component(X2, initial_w, eta)\n",
    "w2 # 求出第二主成分"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 将X2去除在第二主成分上的分量，得到X3\n",
    "X3 = np.empty(X2.shape)\n",
    "for i in range(len(X)):\n",
    "    X3[i] = X2[i] - X2[i].dot(w2) * w2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f9ecbe0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 绘制X3，此时，X3的所有样本点分布在一条直线上\n",
    "ax = plt.axes(projection='3d')\n",
    "ax.scatter3D(X3[:,0], X3[:,1], X3[:,2])\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
